Discrete shock profiles for systems of conservation laws

Journal Article · Sun Jul 01 04:00:00 EDT 1979 · Commun. Pure Appl. Math.; (United States)

DOI:https://doi.org/10.1002/cpa.3160320402· OSTI ID:5435133

Majda, A ^[1]; Ralston, J ^[2]

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1. California, University, Berkeley, Calif.
2. California, University, Los Angeles, Calif.

The existence of discrete shock profiles for difference schemes approximating a system of conservation laws is the major topic studied in this paper. The basic theorem established here applies to first-order accurate difference schemes for weak shocks, this theorem provides necessary and sufficient conditions involving the truncation error of the linearized scheme which guarantee entropy satisfying or entropy violating discrete shock profiles. Several explicit difference schemes are used as examples illustrating the interplay between the entropy condition, monotonicity, and linearized stability. Entropy violating stationary shocks for second-order accurate Lax-Wendroff schemes approximating systems are also constructed. The only tools used in the proofs are local analysis and the center manifold theorem.

• OSTI ID: 5435133
• Journal Information: Commun. Pure Appl. Math.; (United States), Journal Name: Commun. Pure Appl. Math.; (United States) Vol. 32; ISSN CPAMA
• Country of Publication: United States
• Language: English

Related Subjects

657006* -- Theoretical Physics-- Statistical Physics & Thermodynamics-- (-1987)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CONSERVATION LAWS
ENTROPY
FINITE DIFFERENCE METHOD
ITERATIVE METHODS
MATHEMATICS
NUMERICAL ANALYSIS
NUMERICAL SOLUTION
PHYSICAL PROPERTIES
SHOCK WAVES
STABILITY
THERMODYNAMIC PROPERTIES